Question: Multiply the following complex numbers: $({-5-5i}) \cdot ({-5+3i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5-5i}) \cdot ({-5+3i}) = $ $ ({-5} \cdot {-5}) + ({-5} \cdot {3}i) + ({-5}i \cdot {-5}) + ({-5}i \cdot {3}i) $ Then simplify the terms: $ (25) + (-15i) + (25i) + (-15 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 25 + (-15 + 25)i - 15i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 25 + (-15 + 25)i - (-15) $ The result is simplified: $ (25 + 15) + (10i) = 40+10i $